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Math Help - continuous clock

  1. #1
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    Jan 2011
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    continuous clock

    Hello,
    I have no previous experience posting on this forum, but as the course I am taking is entitled Analysis, I hope this is the correct forum.

    I have been given an exercise by my teacher:

    Imagine a clock where the hour hand and the minute hand
    are indistinguishable from each other. Assuming the hands move continuously
    around the face of the clock, and assuming their positions can be measured with
    perfect accuracy, is it always possible to determine the time?

    and I am not sure, what exactly it is I should do here to answere it correctly.
    I have a notion though, that it might involve something like the intermediate value theorem, because if they hands move continously this theorem would apply and therefore it would be possible to always measure the time correctly? But I am not so sure what exactly to "mathematically" do.

    Thanks in advance for any help
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Lero View Post
    Hello,
    I have no previous experience posting on this forum, but as the course I am taking is entitled Analysis, I hope this is the correct forum.

    I have been given an exercise by my teacher:

    Imagine a clock where the hour hand and the minute hand
    are indistinguishable from each other. Assuming the hands move continuously
    around the face of the clock, and assuming their positions can be measured with
    perfect accuracy, is it always possible to determine the time?

    and I am not sure, what exactly it is I should do here to answere it correctly.
    I have a notion though, that it might involve something like the intermediate value theorem, because if they hands move continously this theorem would apply and therefore it would be possible to always measure the time correctly? But I am not so sure what exactly to "mathematically" do.

    Thanks in advance for any help
    You could try an analysis based on the angles of the two hands.
    At 12, they overlap.
    At every hour, the minute hand is vertical and the hour hand will be at a multiple of 30 degrees.

    For any time outside of 12, you could show that at any position,
    the hour hand and minute hand could not possibly be reversed.
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  3. #3
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    Jan 2011
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    how could I show that they could not possibly be reversed? Although I think it is intuitive I am not sure how to show it.
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